angular observables for spin discrimination in boosted · 2 reconstructing angular correlations in...
TRANSCRIPT
JHEP09(2016)036
Published for SISSA by Springer
Received: June 1, 2016
Accepted: August 27, 2016
Published: September 7, 2016
Angular observables for spin discrimination in boosted
diboson final states
Malte Buschmann and Felix Yu
PRISMA Cluster of Excellence & Mainz Institute for Theoretical Physics,
Johannes Gutenberg University, 55099 Mainz, Germany
E-mail: [email protected], [email protected]
Abstract: We investigate the prospects for spin determination of a heavy diboson res-
onance using angular observables. Focusing in particular on boosted fully hadronic final
states, we detail both the differences in signal efficiencies and distortions of differential dis-
tributions resulting from various jet substructure techniques. We treat the 2 TeV diboson
excess as a case study, but our results are generally applicable to any future discovery in
the diboson channel. Scrutinizing ATLAS and CMS analyses at 8 TeV and 13 TeV, we find
that the specific cuts employed in these analyses have a tremendous impact on the discrim-
ination power between different signal hypotheses. We discuss modified cuts that can offer
a significant boost to spin sensitivity in a post-discovery era. Even without altered cuts,
we show that CMS, and partly also ATLAS, will be able to distinguish between spin 0, 1,
or 2 new physics diboson resonances at the 2σ level with 30 fb−1 of 13 TeV data, for our
2 TeV case study.
Keywords: Jets
ArXiv ePrint: 1604.06096
Open Access, c© The Authors.
Article funded by SCOAP3.doi:10.1007/JHEP09(2016)036
JHEP09(2016)036
Contents
1 Introduction 1
2 Reconstructing angular correlations in pp → X, X → V1V2 → 4q 4
2.1 General framework 4
2.2 Phenomenology of jet substructure 5
3 Angular observables in the 4q final state: the 2 TeV case study 8
3.1 Signal benchmarks 8
3.2 ATLAS and CMS analysis cuts at 8 TeV and 13 TeV 9
3.3 Analysis effects and reconstruction 11
4 Angular observables in semi-leptonic final states 19
4.1 ATLAS and CMS semi-leptonic analyses at 8 TeV and 13 TeV 20
4.2 Angular observables in semi-leptonic final states and comparison with fully
hadronic final states 22
5 Projections for model discrimination from 4q final state 25
6 Conclusion 28
A ATLAS 13 TeV background extraction, inclusive diboson selection 29
1 Introduction
The resumption of the Large Hadron Collider (LHC) with proton-proton collisions at
13 TeV has reignited the excitement for a possible discovery of new physics. The higher
energies afforded by the increase in energy during Run 2 also place additional importance
on the need for robust analysis tools to enable such discoveries in the hadronic enviroment
of the LHC. One such suite of analysis techniques is the maturing field of jet substruc-
ture [1–5], which take advantage of large Lorentz boosts of decaying Standard Model (SM)
or new physics (NP) particles to reveal their underlying partonic constituents. Jet sub-
structure tools are also invaluable for mitigating pile-up backgrounds at the LHC, allowing
the ATLAS and CMS experiments to use primary vertex information and jet substructure
methods to discard pile-up contamination of jets resulting from the hard scattering process
of interest [6, 7].
The special utility of jet substructure techniques as new physics discovery tools was
recently highlighted in the ATLAS 8 TeV search for electroweak diboson resonances in fully
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hadronic final states [8]. In this analysis, ATLAS observed a 2.5σ global significance devia-
tion at about 2 TeV in the reconstructed WZ invariant mass distribution. The correspond-
ing CMS 8 TeV analysis [9] does not preclude a possible signal at ATLAS, partly because
the two experiments use different reconstruction methods for tagging boosted, hadroni-
cally decaying W and Z candidates. The most recent 13 TeV results from ATLAS [10]
and CMS [11] in the same fully hadronic diboson decay, however, show no evidence for a
continued excess.
If the excess is a new physics signal, numerous studies are needed to characterize the
resonance and measure the underlying new physics Lagrangian. First, for self-consistency,
the signal must also begin to show up in the semi-leptonic and fully leptonic diboson decays.
Observing the excess in these decays is also critical, though, because the exclusive rates
for the semi-leptonic and fully leptonic modes will help diagnose the underlying W+W−
vs. W±Z vs. ZZ nature of the purported resonance, which is difficult to disentangle using
only hadronic diboson decays. Currently, ATLAS has searches for electroweak diboson
resonances with 8 TeV data in the `ν`` channel [12], ``jj channel [13], and the `νjj chan-
nel [14], which have been combined with the fully hadronic search in ref. [15]. In addition,
CMS has searches with 8 TeV data in the `ν`` channel [16] and `νjj and ``jj channels [17].
We remark, however, that the 2 TeV excess seen by ATLAS in the fully hadronic channel
is only marginally probed by the analyses targetting semi-leptonic diboson decays, after
rescaling the signals that fit the excess by the appropriate leptonic branching fractions [18].
The current situation with 13 TeV data seems to favor the interpretation that the
2 TeV excess was instead a statistical fluctuation, although the data is not conclusive. Both
ATLAS and CMS have retooled their fully hadronic diboson resonance analyses [10, 11] to
focus on the multi-TeV regime, adopting different jet substructure methods than those used
previously during the 8 TeV run. CMS and ATLAS also search in the `νjj channel [11, 19],
respectively, and ATLAS also has performed analyses in the ``jj channel [20] as well as
the ννjj channel [21]. Although the integrated luminosity at 13 TeV is only 3.2 fb−1 for
ATLAS and 2.6 fb−1 for CMS, in comparison to the 20 fb−1 datasets for each experiment
at 8 TeV, naive parton luminosity rescaling from 8 TeV to 13 TeV for the simplest new
physics explanations of the 2 TeV excess point to ATLAS and CMS being at the edge of
NP exclusion sensitivity (see figure 8 of [10], figure 4 of [19], figure 4 of [21], and figures 9
and 10 of [11]).
Beyond the self-consistency requirement to observe the diboson excess in leptonic
channels, various new physics models also predict a new dijet resonance as well as V H
resonances, where V is a massive electroweak boson and H is the Higgs boson [22–26].
The corresponding dijet resonance searches from ATLAS 8 TeV data [27], CMS 8 TeV
data [28], ATLAS 13 TeV data [29] and CMS 13 TeV data [30], as well as WH and ZH
resonance searches with 8 TeV ATLAS data [31], 8 TeV CMS data [32–34], and 13 TeV
ATLAS data [35], have all variously been statistically consistent with the SM background
expectation, which then provide important model-dependent constraints on new physics
interpretations of the 2 TeV excess.
Given the experimental situation, many papers have delved into the model-building
details and phenomenological questions that reconcile the original excess with the currently
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available experimental data. Spin-0 explanations are discussed in context of a Higgs sin-
glet [36], a two Higgs doublet model [37–40], sparticles [41, 42] or composite scalars [43, 44].
Spin-1 proposals include composite vector resonances [45–52], generic and effective field
theory (EFT) models [53–56] as well as heavy W ′ resonances [22–25, 57–69], Z ′ reso-
nances [26, 70–76] or both [77–83]. Other NP scenarios include glueballs [84], excited
composite objects [85], and in generic and EFT models [86–91].
Although the new physics situation with 13 TeV data is less attractive because the
initial dataset does not confirm the excess, the experimental sensitivity with the current
luminosity is nonetheless insufficient to make a final conclusion for the original excess.
Thus the question about whether the excess is a real signal will simply have to wait for
more integrated luminosity.
Apart from the excitement over the original ATLAS diboson excess, however, we are
motivated to consider how jet substructure techniques can be used as post-discovery tools
for resonance signal discrimination. After the Higgs discovery in 2012, the ATLAS and
CMS collaborations began comprehensive Higgs characterization programs, which aim to
measure the couplings, mass, width, spin, parity, production modes, and decay modes of
the Higgs boson. In particular, much of the spin and parity information about the 125 GeV
Higgs boson comes from angular correlations in the h→ 4` decay [92–95], where the Higgs
candidate can be fully reconstructed and all angular observables can be studied.
For the case of a possible 2 TeV resonance X, the exact same analytic formalism for
spin characterization used for h→ 4` [96–101] applies to X → V V → 4q [87], which natu-
rally opens up the possibility of designing a jet substructure analysis that targets spin and
possibly parity characterization of the X resonance. The X → V V → 4q situation is more
difficult, however, because it is a priori unknown how well the angular correlations in the
final state quarks are preserved after the important effects from showering and hadroniza-
tion, detector resolution, jet clustering, and hadronic W and Z boson tagging are included.
In contrast, the h → 4` decay can be analyzed without the complications from quantum
chromodynamics (QCD) and only need to account for virtual γ∗/Z interference and mild
detector effects [102–104]. Our study provides a thorough investigation of these important
and difficult complications, and we connect distortions in angular observables with specific
jet substructure cuts. Our results show significant differences between the ATLAS and
CMS 8 TeV and 13 TeV analyses regarding post-discovery signal discrimination. They also
provide useful templates for understanding the differences in sensitivity of the current jet
substructure methods to tranversely or longitudinally polarized electroweak gauge bosons.
We also make projections for how well the current slate of diboson reconstruction methods
will perform with 30 fb−1 of LHC 13 TeV integrated luminosity. The next obvious course of
action would be to design a jet substructure method optimized for both signal significance
and post-discovery spin discrimination using the extracted subjets. We leave such work
for the future and instead focus on determining the viability of existing jet substructure
techniques with regards to spin determination.
In section 2, we review the angular analysis framework for characterizing a resonance
decay. We also review the broad classes of jet substructure methods and general challenge
of reconstructing angular correlations in the fully hadronic final state and the hadronic
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environment. In section 3, we detail the 2 TeV case study signal benchmarks, review the
8 TeV and 13 TeV ATLAS and CMS fully hadronic boosted diboson decay selection criteria,
and show the differential distributions after implementing these analyses. We also identify
specific jet substructure cuts to their effects on the differential distributions. We evaluate
the semileptonic analyses in section 4 in a similar manner, highlighting the new distortions
that arise when considering semileptonic final states. We present our expectations for
model discrimination with 30 fb−1 of LHC 13 TeV data in section 5 and briefly discuss
improvements in jet substructure analyses targetting signal discrimination. We conclude
in section 6. In appendix A, we discuss the inclusive background determination for the
ATLAS 13 TeV analysis neeeded in our 13 TeV, 30 fb−1 projections.
2 Reconstructing angular correlations in pp → X, X → V1V2 → 4q
2.1 General framework
In this section, we review the general framework for studying angular correlations of a
resonance X decaying to two intermediate vector bosons that subsequently decay to four
light quarks. We will work in the X rest frame and orient the incoming partons along
the +z and −z axes as usual. We also neglect the masses of our final state particles,
which reduces the nominal sixteen final state four-momentum components to twelve. Four-
momentum conservation in the rest frame of the resonance further reduces the number of
independent components to eight. Finally, the overall system can be freely rotated about
the +z axis, so we can completely characterize the kinematics of the system with seven
independent variables, which are five angles and the two intermediate vector masses. If
the resonance mass is not known, it also counts as an independent quantity. Finally, if
the final state particles are not massless, then their four masses also have to be used as
independent variables.
The five angles, known as the Cabibbo-Maksymowicz-Dell’Aquila-Nelson angles [96–
99], the two intermediate vector masses, and the resonance mass are hence completely
sufficient to describe the kinematics of the pp→ X → V1V2 → (p1p2)(p3p4). These angles
are shown in figure 1 and are given by
cos θp1 = −pp1 · pV2 , ΦV1 =~pV1 · (n1 × nsc)
|~pV1 · (n1 × nsc)|arccos(n1 · nsc) ,
cos θp3 = −pp3 · pV1 , Φ =~pV1 · (n1 × n2)
|~pV1 · (n1 × n2)|arccos(−n1 · n2) ,
cos θ∗ = pV1 · zbeam , (2.1)
where V1 and V2 are the two bosons, X is the resonance, zbeam is the direction of the beam
axis and
n1 =~pp1 × ~pp2
|~pp1 × ~pp2 |, n2 =
~pp3 × ~pp4
|~pp3 × ~pp4 |, and nsc =
zbeam × ~pp1
|zbeam × ~pp1 |. (2.2)
The intermediate vectors V1 and V2 are reconstructed by pV1 = pp1 + pp2 , pV2 = pp3 + pp4 ,
and the resonance X is formed by pX = pV1 + pV2 . The angle cos θp1 (cos θp3) is calculated
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Figure 1. Representation of the Cabibbo-Maksymowicz-Dell’Aquila-Nelson angles defined in
eq. (2.1).
with the respective four-momenta boosted into the rest frame of particle V1 (V2), whereas
all other angles are computed in the rest frame of particle X. Additionally, we define the
angle Ψ = ΦV1 + Φ/2 to supersede ΦV1 , where Ψ is the average azimuthal angle of the two
decay planes.
Resonances with different spins will produce different angular correlations among the
decay products. A full set of analytic expressions for different resonance hypotheses and
the subsequent angular correlations in the X → V1V2 → 4 fermion final state can be found
in ref. [101], which we do not reproduce here. We have verified the analytic expressions
in ref. [101] by comparing to parton level Monte Carlo results for different resonant spin
hypotheses. Our full discussion of Monte Carlo signal samples and analysis of angular
correlations analysis is given in section 3.
2.2 Phenomenology of jet substructure
While the angles defined in figure 1 underpin any analysis aimed at spin characterization of
a given resonance, the corresponding differential distributions are expected to be smeared
and skewed after accounting for showering and hadronization, detector resolution effects, jet
clustering methods, and jet substructure cuts. Of these effects, the distortions introduced
by jet clustering methods and jet substructure cuts are the most pernicious.
The usual goal for jet substructure techniques is to isolate the partonic constituents of
a given wide angle jet that captures the decay products of a boosted parent, like a W , Z, h,
or t resonance. As a result, different methods have been developed to maximize the tagging
efficiency of these parent particles while simultaneously minimizing the mistag rate from
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QCD or other backgrounds [3, 4]. In this endeavor, angular observables have played an
implicit role to help improve the overall tagging efficiency of a given parent particle over the
QCD background, but on the other hand, recovering the full phase space of resonance decay
products will be key for post-discovery signal discrimination. Moreover, understanding how
angular observables are distorted by jet substructure cuts is also necessary to optimize
signal hypothesis testing in a post-discovery scenario.
To this end, we review the main jet substructure methods to extract subjets from fat
jets, as well as jet substructure techniques used for background discrimination. Variants
of these methods are all used, as we will see, in the most recent ATLAS and CMS 8 TeV
and 13 TeV analyses [8–11].
Mass-drop filter technique. The jet grooming procedure used in the 8 TeV ATLAS
analysis [8] is known as mass-drop filtering [1]. An original fat jet, reconstructed with
the Cambridge-Aachen (C/A) cluster algorithm [105], is “unclustered” in reverse order.
Each step of the unclustering gives a pair of subjets that is tested for both mass-drop and
momentum balance conditions. The procedure is stopped if the two conditions are satisfied.
The mass-drop criterion requires each subjet to satisfy µi ≡ mi/m0 ≤ µf for a given
parameter µf , where mi is the subjet mass and m0 is the original jet mass. The 8 TeV
ATLAS hadronic and semi-leptonic diboson searches use µf = 1, which effectively means
no mass-drop cut is applied.
The subjet momentum balance condition imposes a minimum threshold on the relative
pT and ∆R of each subjet, according to
√y = min(pT1 , pT2)
∆R
m0≥ √ymin , (2.3)
where pTi is the transverse momentum of each subjet ji, ∆R =√
(∆φ)2 + (∆η)2 is their
angular distance, and√ymin is a parameter controlling the threshold. To see how eq. (2.3)
acts as a cut on the subjet momentum balance, we rewrite eq. (2.3) using
m20 = 2pT1pT2 (cosh(∆η)− cos(∆φ)) ≈ pT1pT2(∆R)2 , (2.4)
which holds as long as the rapidity difference ∆η and azimuthal separation ∆φ are small.
Using this approximation, we see that the√ymin cut is indeed a subjet momentum balance
cut as advertised,
y ≈ { min(pT1 , pT2)}2
pT1pT2
=pT, min
pT, max≥ ymin . (2.5)
At each stage of the unclustering, if the pair of subjets under consideration satisfies√y ≥
√ymin, the procedure terminates and the total four-momentum of the subjets are used as
the W or Z boson candidate. If the subjets fail the cut, the softer subjet is discarded and
the unclustering procedure continues.
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Pruning. In contrast to mass-drop filtering, which recursively compares subjets to the
original fat jet kinematics, the jet pruning method [106, 107], which is used in the 8 TeV
CMS analysis [9], tests each stage of the reclustering for sufficient hardness and discards soft
recombinations. In this way, each stage of the reclustering offers an opportunity to remove
constituents from the final jet, instead of simply incorporating the soft contamination into
the widest subjets.
Concretely, in the jet pruning method, the constituents of a fat jet are reclustered
using the C/A algorithm if they are sufficiently balanced in transverse momentum and
sufficiently close in ∆R. The transverse momentum balance condition is dictated by a
minimum requirement on the hardness z, defined by
z = min
(pTipTp
,pTjpTp
), (2.6)
where pTp is the sum of the tranverse momentum of the psuedojets i and j. Note that z is
related the momentum fraction y from eq. (2.5) via
y ≈pT, min
pT, max=
z
1− z. (2.7)
In addition to having sufficient hardness, the two pseudojets must also be closer in ∆R
than a parameter Dcut, given by
∆Rij > Dcut ≡morig
pT, orig, (2.8)
where morig and pT, orig are the invariant mass and transverse momentum of the original
fat jet. If either the hardness or the ∆R cut fails, then the softer pT pseudojet is discarded.
The C/A reclustering procedure continues until all the constituents of the original fat jet
are included or discarded.
N-subjettiness. The N -subjettiness variable [108, 109] is used by CMS in their 8 TeV
and 13 TeV analyses [9, 11] to help suppress QCD multi-jet backgrounds and improve
selection of hadronic W and Z candidates. The N -subjettiness is defined as
τN =1
d0
∑k
pTk min(∆R1,k, . . . ,∆RN,k) , (2.9)
where pTk is the transverse momentum of the kth constituent of the original jet and ∆Rn,kis the angular distance to the nth subjet axis. The set of N subjets is determined by
reclustering all jet constituents of the unpruned jet with the kT algorithm and halting
the reclustering when N distinguishable pseudojets are formed. Here, d0 ≡∑
k pTkR0 is
a normalization factor for τN , where R0 is the cone size of the original fat jet. For the
boosted hadronic W and Z analyses, the ratio τ21 = τ2/τ1 is computed, where the signal
W and Z candidates tend toward lower τ21 values, whereas the QCD background peaks at
higher values.
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JHEP09(2016)036
Trimming. The 13 TeV ATLAS analysis [10] was reoptimized for multi-TeV scale dibo-
son sensitivity and adopts the trimming procedure [110] instead of the earlier mass-drop
filtering technique. Trimming takes a large radius fat jet and reclusters the constituents
with the kT cluster algorithm [111] using distance parameter R = 0.2. Of the resulting set
of subjets, those kept must satisfy
pTjpTJ
> zmin , (2.10)
where j denotes the subjet and J the original fat jet. The four-momentum sum of all
remaining subjets is used as a W or Z candidate. For an ideal W or Z decay, with exactly
two final subjets, the above condition translate directly to the same balance criteria as the
filtering technique,
y ≈pT, min
pT, max≥ ymin =
zmin
1− zmin. (2.11)
Note, however, that this algorithm does not consider pairs of subjets as the pruning or
filtering techniques do. Thus, it is possible to obtain more than two subjets and hence
additional cuts, such as energy correlation function cuts, are needed to determine whether
the trimmed jet has a two-prong substructure.
Energy correlation functions. The ATLAS 13 TeV analysis [10] uses energy correla-
tion functions [112–114] to characterize the number of hard subjets in their set of trimmed
jets. The relevant 1-point, 2-point and 3-point energy correlation functions are
e(β)1 =
∑1≤i≤nJ
pTi ,
e(β)2 =
∑1≤i<j≤nJ
pTipTj∆Rβij ,
e(β)3 =
∑1≤i<j<k≤nJ
pTipTjpTk∆Rβij∆Rβik∆R
βjk , (2.12)
where the sums are performed over jet constituents and β is a parameter weighting the
angular separations of constituents against their pT fractions. Since the sums are performed
over jet constituents, the energy correlation functions are independent of any jet algorithm.
An upper limit is set on the ratio of the function
D(β)2 =
e(β)3
(e
(β)1
)3
(e
(β)2
)3 , (2.13)
where the ATLAS collaboration uses β = 1 in their 13 TeV analysis.
3 Angular observables in the 4q final state: the 2 TeV case study
3.1 Signal benchmarks
We consider spin-0, spin-1 W ′, spin-1 Z ′, spin-1 WR, and spin-2 new physics resonances
as possible candidates for the 2 TeV excess from the ATLAS 8 TeV analysis [8]. The
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JHEP09(2016)036
spin-0 possibility is an ad-hoc real scalar model built from the Universal FeynRules Out-
put [115] implementation of the SM Higgs effective couplings to gluons in MadGraph
v.1.5.14 [116], and is included only as an example of a heavy real scalar that couples dom-
inantly to longitudinal vector bosons. The spin-1 W ′ and spin-1 Z ′ possibilities are based
on the Heavy Vector Triplet model [47, 117], whose phenomenology related to the ATLAS
2 TeV diboson excess was described in detail in ref. [47]. The spin-1 WR explanation is
taken from the UFO model files that accompany ref. [25]. The spin-2 heavy graviton reso-
nance is adapted from a Randall-Sundrum scenario [118, 119] as a MadGraph model file
implementation [120].
Each of these signal possibilities is generated as an on-shell resonance in MadGraph
with subsequent decays to massive electroweak diboson and then final state SM fermions.
These parton level events are then showered and hadronized with Pythia v.8.2 [121], pro-
cessed through Delphes v.3.1 [122] for detector simulation, and clustered into jets using
the FastJet v.3.1.0 [123] as each ATLAS or CMS analysis requires. Because Delphes
does not include parametrized detector simulation of jet constituents, which are the basis
for studying jet substructure and angular correlations between subjets, we also post-process
the jet constituents to smear their pT , φ, and η to mimic detector resolution effects: the
constituent smearing parameters are rescaled by the respective energy fraction of the con-
stituent compared to the full jet.
We simulate QCD dijet background with Pythia v.8.2 [121]. The subsequent event
evolution is the same as described above.
3.2 ATLAS and CMS analysis cuts at 8 TeV and 13 TeV
We recast the ATLAS and CMS searches for heavy resonances with hadronic diboson
decays at 8 TeV [8, 9] and 13 TeV [10, 11]. As the angular correlations in term of the
parameterization of section 2 are skewed by the actual analyses, we briefly summarize the
basic selection criteria for the different searches.
4q Final State by ATLAS at 8 TeV. In the fully hadronic ATLAS search for diboson
resonances at 8 TeV, jets are clustered with the C/A algorithm with radius R = 1.2, and
events must have two jets with pT > 20 GeV and |η| < 2.0. If there are electrons with
ET > 20 GeV and |η| < 1.37 or 1.52 < |η| < 2.47, or if there are muons with pT > 20 GeV
and |η| < 2.5, the event is vetoed. Events must also have /ET < 350 GeV.
The two fat jets are then filtered with ymin = 0.04. The constituents of the two subjets
of the groomed jet are then reclustered again with the C/A algorithm but with a smaller
cone size of R = 0.3. The up to three highest-pT jets, which we will call filtered jets, are
used to reconstruct the W or Z boson candidate. Having reconstructed the ungroomed,
groomed, and filtered jets, further event selection cuts are applied. The rapidity difference
between the ungroomed jets must satisfy |yJ1 − yJ2 | < 1.2. Additionally, the pT asym-
metry of ungroomed jets must be small, (pT, J1 − pT, J2) / (pT, J1 + pT, J2) < 0.15. The
ungroomed and corresponding groomed and filtered jets are tagged as a W or Z boson if
they fulfill the following three criteria:
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JHEP09(2016)036
• The pair of subjets of the groomed jet must satisfy a stronger transverse momentum
balance requirement, y ≥ ymin = 0.2025.
• The number of charged tracks associated to the ungroomed jet has to be less than
ntrk < 30. Only well-reconstructed tracks with pT ≥ 500 MeV are used.
• The W or Z boson candidates, reconstructed from the filtered jets, are finally tagged
as a W and/or Z, if their invariant mass fulfills |mJ −mV | < 13 GeV. Here, mV is
either 82.4 GeV for a W boson or 92.8 GeV for a Z boson, as determined ATLAS full
simulation.
Finally, the event is required to have the two highest-pT jets be boson-tagged and mJJ >
1.05 TeV.
4q final state by CMS at 8 TeV. The CMS 8 TeV analysis uses jet pruning to recon-
struct a diboson resonance. Jets are reconstructed with the C/A algorithm using R = 0.8,
and events must have at least two jets with pT > 30 GeV and |η| < 2.5, where the two
leading jets must satisfy |∆η| < 1.3 and mJJ > 890 GeV. The two jets are pruned with
zmin = 0.1 (roughly equivalent to ymin = 0.11) and the corresponding W/Z candidate must
satisfy 70 GeV < mJ < 100 GeV. Jets are further categorized according to their purity
using the N -subjettiness ratio τ21, where high-purity W/Z candidates have τ21 < 0.5 and
low-purity W/Z candidates have 0.5 < τ21 < 0.75. The diboson resonance search requires
at least one high-purity W/Z jet, and the second W/Z can be either high- or low-purity.
4q final state by ATLAS at 13 TeV. In ATLAS 13 TeV analysis, events are again
vetoed if they contain electrons or muons with pT > 25 GeV and |η| < 2.5, and events
must have /ET < 250 GeV. In contrast to earlier, though, jets are now clustered using
the anti-kT cluster algorithm [124] with R = 1.0, and events must have two fat jets with
pT > 200 GeV, |η| < 2.0 and mJ > 50 GeV. The leading jet must have pT > 450 GeV, the
invariant mass of the two fat jets must lie between 1 TeV and 2.5 TeV, and the rapidity
separation must be small, |yJ1 − yJ2 | < 1.2. Furthermore, the leading two jets must also
have a small pT asymmetry, (pT, J1 − pT, J2) / (pT, J1 + pT, J2) < 0.15.
Jets are then trimmed, instead of filtered, by reclustering with the kT algorithm using
R = 0.2 and using hardness parameter zmin = 0.05, and the energy correlation functions
for D(β=1)2 are then calculated on the trimmed jets to help distinguish W bosons, Z bosons,
and multijet background. The upper limit on D2 varies for W and Z candidates as well as
the pT of the trimmed jet: to implement this D2 cut, we linearly interpolate between the
two cut values, D2 = 1.0 at pT = 250 GeV and D2 = 1.8 at pT = 1500 GeV, quoted in their
analysis. The trimmed jets are tagged as bosons if they fulfill two final criteria: Ntrk < 30
for charged-particle tracks associated with the ungroomed jet and |mJ −mV | < 15 GeV,
where mV = 84 GeV for a W boson and mV = 96 GeV for a Z boson.
4q final state by CMS at 13 TeV. The CMS 13 TeV analysis shares many of the
same selection criteria as their 8 TeV analysis, with the following adjustments. The two
anti-kT , R = 0.8, pT > 30 GeV jets must now lie within |η| < 2.4. The pseudorapidity
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JHEP09(2016)036
separation between the two jets must again satisfy |∆η| < 1.3, and the minimum invariant
mass cut on mJJ is raised to 1 TeV. The two jets are again pruned with zmin = 0.1 and
the pruned jet mass window is widened, allowing 65 GeV< mW/Z < 105 GeV. Finally,
the N -subjettiness ratio τ21 is again calculated, where high-purity W/Z jets must have a
slightly harder requirement, τ21 ≤ 0.45, and low-purity W/Z jets satisfy 0.45 < τ21 < 0.75.
The event must have at least one high-purity W/Z jet and is classified as high-purity or
low-purity according to the second jet.
3.3 Analysis effects and reconstruction
We implement the fully hadronic ATLAS and CMS diboson searches on the signal samples
presented in section 3.1, and we extract the angular observables reviewed in section 2.1
from the subjets of the reconstructed W/Z-tagged boson. Since W/Z discrimination is
very difficult in this final state, we merge the cos θp1 and cos θp3 distributions into a single
differential distribution labeled cos θq and do not differentiate between W and Z candidates.
We also recognize that these analyses do not attempt to distinguish quarks from anti-
quarks, hence we randomly assign the p1 and p2 labels (or p3 and p4 labels) to subjets of
a given W/Z candidate, which renders the signs of different angles ambiguous. Finally,
we merge the high-purity and low-purity tagged events in the CMS analyses to ensure our
angular sensitivity analysis has reasonable statistics.
We find that of the angles defined in section 2, the main discrimination power between
different spin scearios comes from cos θ∗, cos θq and Ψ. In the remainder of this section, we
will present the individual differential shapes for the different Monte Carlo samples and ex-
perimental studies, and explain how they are skewed by the respective event selection and
jet substructure cuts. All of our figures show both parton and reconstruction level unit-
normalized distributions for the different signal samples and QCD multijet background,
where all showering, hadronization, detector resolution, jet reconstruction, and substruc-
ture analysis effects have been included in the reconstructed differential distributions.
Differential shape of cos θ∗. We first show the angular observable cos θ∗ in figure 2
for various spin-0, spin-1, and spin-2 signal benchmarks and the QCD background after
implementing the ATLAS 8 TeV (upper left), CMS 8 TeV (upper right), ATLAS 13 TeV
(lower left), and CMS 13 TeV (lower right) analyses. This angle measures the alignment of
the vector bosons from X decay with the beam axis, if we use the threshold approximation
to identify the X rest frame with the lab frame. We see significant discrimination power
at parton level (thin lines) between the different signal benchmarks, especially between
the spin-0 and spin-2 signals compared to the spin-1 benchmark. The extra oscillations
in the spin-2 signal, however, are lost when comparing the reconstruction level (thick
lines) distributions, leaving only the overal concavity of the spin-1 distribution the main
discriminant from the spin-0, spin-2, and QCD background shapes. Comparing parton
level to reconstruction level results for each signal sample, we see the experimental analyses
cause significant hard cuts in cos θ∗, effectively requiring | cos θ∗| . 0.55 for ATLAS and
| cos θ∗| . 0.6 for CMS, and we also see a deficit of events around cos θ∗ ≈ 0 is induced by
each analysis, most notably in the ATLAS 13 TeV analysis.
– 11 –
JHEP09(2016)036
Figure 2. Comparison of the cos θ∗ angle between MC parton level results (thin lines) and recon-
struction of showered events via jet substructure (thick lines) for the ATLAS (left) and CMS (right)
hadronic diboson search at 8 TeV (top) and 13 TeV (bottom). Each distribution is unit-normalized.
We can identify the sharp cliffs in the | cos θ∗| distribution with the cut on the maximum
pseudorapidity difference |∆η| between the two fat jets, since the θ∗ angle is directly related
to the pseudorapidity via η = − log tan(θ/2). Therefore cos θ∗ can be rewritten in the X
rest frame as
| cos θ∗| = cos(
2 arctan e−|∆η|
2
)= tanh
|∆η|2≤ tanh
|∆ηmax|2
. (3.1)
Given |∆ymax| = 1.2 at ATLAS and |∆ηmax| = 1.3 at CMS, and since differences in
pseudorapidity are invariant under longitudinal boosts, we therefore expect sharp cuts at
| cos θ∗| ≈ 0.54 and 0.57, respectively, where the steepness of the cliff is only spoiled by the
net transverse momentum of the X resonance in the lab frame.
– 12 –
JHEP09(2016)036
R∆0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.2
0.4
0.6
0.8
1
1.2
1.4
0
5
10
15
20
25
30
0
0.1
0.2
0.3
0.4
0.5
0.6
η∆Rd∆dσ2d σ
1
η∆ *)|θ|cos(
Figure 3. Spin-1 W ′ parton level correlation of the angular separation ∆R between the W/Z decay
products and the rapidity difference ∆η of the two W ′ → WZ fat jets, where the left band shows
the W decay products and the right band shows the Z decay products, and the shading shows the
relative event weight. This correlation holds also for other spin scenarios. The ∆η axis is translated
to a | cos θ∗| axis according to eq. (3.1).
The deficit of events around cos θ∗ ≈ 0 is a direct result of the angular scale chosen
for the jet substructure analysis, where a larger angular scale causes a stronger sculpting
behavior around cos θ∗ ≈ 0. We know from eq. (3.1) that small cos θ∗ is identified with
small ∆η between the two fat jets, and we also show in figure 3 the parton level correlation
between ∆η for the two fat jets and ∆R of the resulting W and Z decay products for a
spin-1 W ′ example. Other signal samples would show a similar correlation, albeit with
only one W (left color band) or Z (right color band) as appropriate. The bulk of the W/Z
subjets lie at ∆R ≈ 2mW/Z/(1 TeV) as expected, where 1 TeV is a rough estimate of the
W and Z transverse momenta when the vector bosons are central, but we also see a clear
correlation between larger ∆η separation between the fat jets and the corresponding ∆R
of the resulting subjets. As ∆η grows, the vector bosons from the W ′ decay become more
forward, and thus the corresponding pT of each vector boson decreases, leading to larger
∆R separation of their subjets.
As a result of this correlation, using a large fixed angular scale during jet substructure
reclustering leads to a deficit of events with small ∆η separation between fat jets and
hence leads to the sculpting effect around cos θ∗ ≈ 0 observed in figure 2. A relatively large
angular scale for subjet clustering will merge nearby partons together, and the resulting
event will not have the requisite subjets to define the cos θ∗ angle and fail the reconstruction
of angular observables. The ATLAS 13 TeV analysis has the most pronounced deficit of
events around cos θ∗ ≈ 0, since this analysis uses a fixed radius of R = 0.2 during trimming.
Most notably, using an angular scale of R = 0.2 during subjet clustering causes most of
the quarks to merge into a single subjet, which severely limits the viability of such a subjet
identification technique for a post-discovery study of angular correlations. We remark that
– 13 –
JHEP09(2016)036
the D(β=1)2 discriminant also used in the ATLAS 13 TeV analysis to identify a prevalence of
two-prong energy correlations compared to one-prong and three-prong energy correlations
fails to ameliorate the situation, as the events with the strongest two-prong behavior would
still need to be reclustered to identify the appropriate subjets for angular observable studies.
Differential shape of cos θq. The second main discriminant between different spin
signal hypotheses is the cos θq angle, shown in figure 4, which combines the cos θp1 and
cos θp3 angles defined in section 2. This angle measures the alignment of the outgoing
quark with the boost vector of its parent vector in the parent rest frame, and since each
event has two vector candidates, each event contribues twice to the distribution. Again
we first focus on the parton level results (thin lines), which show that the spin-2 RS
graviton hypothesis has the opposite concavity to the spin-0 and spin-1 signals. We note
that the spin-2 resonance dominantly couples to tranversely polarized electroweak bosons,
while the spin-0 and spin-1 resonances dominantly couple to longitudinal bosons. Hence,
the pronounced difference in shape between the signals is a realistic proxy for studying the
sensitivity of different jet substructure analyses to the polarization of W and Z bosons. For
longitudinal bosons, the expected analytic shape of the cos θq distribution is 34
(1− cos2 θq
),
while the shape is 38
(1 + cos2 θq
)for transverse bosons [101]. We remark that enhancing
sensitivity to either the center or edges of the cos θq distribution will emphasize sensitivity
to longitudinal or transverse gauge bosons, respectively. These results also agree with an
earlier analysis by CMS [125], but we carry the analysis further by studying multiple state-
of-the-art jet substructure techniques to understand the impact of vector boson polarization
on the resulting reconstruction efficiency.
Turning to the reconstructed angular distributions (thick lines) in figure 4, we again see
the full phase space of the parton decays gets significantly molded by the experimental anal-
yses, where events close to cos θq ≈ ±1 are cut away. In contrast to the sharp cliffs in cos θ∗,
though, the cos θq distribution exhibits a milder transformation, and start and strength of
the deviations depend strongly on the individual analysis. At 8 TeV, ATLAS shows a re-
versal point at cos θq ≈ ±0.6, whereas the CMS reversal point is cos θq ≈ ±0.8. We also
observe a deficit of events with cos θq ≈ 0, most notably in the ATLAS 13 TeV analysis.
In order to understand the behavior around cos θq ≈ ±1, we derive an approximate
relation between cos θq and the subjet pT ratio y. Identifying cos θq with cos θp1 for the
moment, we write cos θq ≡ pp1 · pV2 from eq. (2.1), where the p1 and V2 four-momenta are
boosted to the V1 rest frame. If we assume threshold production of X, then the X rest
frame is identified with the lab frame, and the two vectors V1 and V2 are completely back-
to-back in both frames. Hence, pV2 in the V1 rest frame can be replaced by the (negative)
boost direction −pV1 going from the lab frame to the V1 rest frame. If we now take the
limiting case that V1 and V2 have no longitudinal momentum, then we are left with six
four-momentum components of p1 and p2, which are the decay products of V1, subject to
four constraints: (p1 + p2)2 = m2V1
, p21 = p2
2 = 0, and y = pT2/pT1 given by the ymin cut
parameter. We choose the two remaining free parameters to be the transverse momentum
of the boson, pT, V1 and the angle between the decay plane spanned by p1 and p2 relative
to the transverse plane. We have three planes: the plane spanned by the beam axis and
– 14 –
JHEP09(2016)036
Figure 4. Comparison of the cos θq angle between MC parton level results (thin lines) and re-
construction of showered events via jet substructure (thick lines) for the ATLAS (left) and CMS
(right) hadronic diboson search at 8 TeV (top) and 13 TeV (bottom).
the V1 boson, the transverse plane, and the decay plane spanned by p1 and p2, where the
common axis of intersection is the V1 transverse momentum vector.
For the limiting case that the decay plane spanned by p1 and p2 aligns with the
transverse plane, the cut on y provides a lower bound on | cos θq|, while the case when the
decay plane aligns with the plane spanned by the beam axis and the V1 boson provides
an upper bound on | cos θq|, where we can only bound | cos θq| because we order the two
subjets in pT . These lower and upper limits are1
pT, V√m2V + p2
T, V
1− y1 + y
≤ | cos θq| ≤
√m2V + p2
T, V
pT, V
1− y1 + y
. (3.2)
1It is easiest to derive these limits by performing an azimuthal rotation of the system to fix the V1
transverse momentum in the y direction.
– 15 –
JHEP09(2016)036
Note that the upper bound can in principle exceed 1, and at this point, for a given pT, Vand y, the solution with the decay plane aligned with the beam axis becomes unphysical
and a rotation of the decay plane away from the beam axis is needed to obtain a physical
solution. If we relax the initial conditions and allow longitudinal boosts of the system,
the resulting y cut will, by construction, project out only the transverse components of
the boost needed to transform the lab frame into the rest frame of V1. This smears the
expression in eq. (3.2) for both the upper and lower limits.
Nevertheless, we can see that in the limit pT, V � mV ,
| cos θq| ≈1− y1 + y
≤ 1− ymin
1 + ymin. (3.3)
For ymin = 0.20, 0.11, or 0.05 for the ATLAS 8 TeV, CMS, and ATLAS 13 TeV analyses,
respectively, we expect edges in the | cos θq| distribution at approximately 0.66, 0.80, and
0.90. As mentioned before, the analytic calculation above requires assumptions about the
necessary boost to move from the lab frame to the V1 rest frame and taking pT, V � mV ,
and if these assumptions are violated, the upper limit on | cos θq| can be exceeded.
This discussion explains the results in figure 4, except for the ATLAS 13 TeV analysis,
where many more events are lost then simply those beyond the derived edge at | cos θq| =0.9. This is because the ATLAS 13 TeV imposes an effectively tighter ymin criteria via the
D(β=1)2 discriminant, which we demonstrate in figure 5. We see that an event with a low
subjet pT ratio would generally have a large value of D(β=1)2 and thus be removed given
the D2 cut. As a reminder, the D2 cut parameter varies from D2 = 1.0 for a trimmed jet
of pT = 250 GeV to D2 = 1.8 for pT = 1500 GeV, which corresponds to ymin ≈ 0.1–0.2, in
agreement with the resulting sculpting seen in figure 4.
Finally, the deficit of events with cos θq ≈ 0 is the same sculpting effect as seen before
around cos θ∗ ≈ 0. In figure 6, we show the correlation between ∆R of the W/Z decays and
the ratio of quark transverse momentum y for parton-level W ′ → WZ events. As before,
the left band shows the W± daughter partons and the right band shows the Z daughter
quarks. Since using a large ∆R during subjet finding causes the W/Z decay partons to
be merged, events with large y are more likely to be removed from the event sample by
subsequent kinematic cuts. Using eq. (3.3), we can relate y to an effective cut on cos θq,
which explains the deficit of events seen around cos θq ≈ 0 in figure 4, most notably in the
lower left panel for the ATLAS 13 TeV analysis.
Differential shape of Ψ. As shown in figure 7, the differential distribution in the angle
Ψ is flat for all spin hypotheses except for the spin-2 resonance.2 We will thus focus on
explaining the behavior of the spin-2 scenario. In this distribution, we expect amplitudes
proportional to 1 and cos (4Ψ), where the respective amplitudes at parton level depend
on the helicity states of the vector bosons and the production level partons [100, 101]. A
cos (2Ψ) contribution would only appear when particles and anti-particles of the V decay
2Recall Ψ = ΦV1 +Φ/2 is the average azimuthal angle of the two decay planes formed by the vector boson
decay products. Also, note that the lower left panel showing the ATLAS 13 TeV analysis is dominated by
statistical fluctuations, which occurs because the R = 0.2 substructure angular scale has poor efficiency at
finding four distinct subjets needed to reconstruct the two decay planes.
– 16 –
JHEP09(2016)036
=1)β(
2D0 0.5 1 1.5 2 2.5 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
1
2
3
4
5
60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
=1)β(
2dydD
σ2d σ1
y )|qθ|cos(
Figure 5. Correlation between the energy correlation function D(β=1)2 and the ratio of transverse
momentum y of the two leading subjets, where the shading shows the relative event weight. All
analysis cuts of the ATLAS 13 TeV analysis are applied, except the cut on D(β=1)2 itself. This
particular plot is based on the spin-1 W ′ model, but the correlation seen holds also for other spin
scenarios. The y axis is translated to a | cos θq| axis according to eq. (3.3).
R∆0.1 0.15 0.2 0.25 0.3 0.35 0.40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
2
4
6
8
10
12
14
16
18
20
22
240
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
Rdy∆dσ
2d σ1
y )|qθ|cos(
Figure 6. Spin-1 W ′ parton level correlations of the angular separation ∆R between the W/Z
decay products and their ratio in transverse momentum y, where the shading shows the relative
event rate. This basic correlation holds also for other spin scenarios. The y axis is translated to an
approximate | cos θq| axis according to eq. (3.3).
can be distinguished. Curiously, the differential distribution of Ψ after cuts causes the
cos (4Ψ) amplitude to increase. This is related to the same two cuts on ∆ηJJ, max and
subjet pT ratio ymin, which already skewed the cos θ∗ and cos θq angle.
– 17 –
JHEP09(2016)036
Figure 7. Comparison of the Ψ angle between MC parton level results (thin lines) and reconstruc-
tion of showered events via jet substructure (thick lines) for the ATLAS (left) and CMS (right)
hadronic diboson search at 8 TeV (top) and 13 TeV (bottom).
We can analytically determine the differential shape of the Ψ distribution as a function
of the cut values on ∆ηJJ, max and ymin, using the fully differential results in ref. [101]. The
normalized shape can be expressed as
1
σ(spin-2)
dσ(spin-2)
dΨ=
1
2π−A(ymin,∆ηmax) cos(4Ψ) , (3.4)
with
A =1
24πF+−
(1 + 4ymin + y2
min
)2(5fqq − 1)(8 + 6 cosh ∆ηmax + cosh 2∆ηmax)
/(3.5)[
F+−(1 + ymin + y2
min
)2 ((5fqq + 1)(1 + 2 cosh ∆ηmax) + 2 cosh 2∆ηmax
)+ F00
(1 + 4ymin + y2
min
)2(−15fqq + 8 + 6 cosh ∆ηmax + cosh 2∆ηmax)
].
– 18 –
JHEP09(2016)036
maxη∆
0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
miny
ATLAS
CMS
0.07 0.065 0.06 0.055 0.05
0.045
0.04
0.035
0.03
0.025
0.02
) amplitude at 8 TeVΨcos(4
maxη∆
0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
miny
CMS
0.015
0.02
0.025
0.030.0350.04
) amplitude at 13 TeVΨcos(4
Figure 8. Expected cos(4Ψ) amplitude A (contours) for a spin-2 resonance at 8 TeV (left) and
13 TeV (right) as function of the cut parameter ymin and ∆ηJJ, max, as shown in eq. (3.5). We use
F+− = F−+ = 45.8% and F00 = 7.8%, as determined from our underlying Monte Carlo simulation,
and fqq = 65.5% and fqq = 45.0% for 8 TeV and 13 TeV, respectively. We also show the respective
working points of ATLAS and CMS, except for ATLAS at 13 TeV, where the effective ymin is not
a fixed parameter.
Here, Fλ1λ2 is the fraction of events with two gauge bosons having a helicity λ1 and λ2
respectively, and fqq is the production fraction from qq initial state quarks. From our
Monte Carlo simulation at 8 TeV, we find F+− = F−+ = 45.8%, F00 = 7.8% and 0.6%
others, and thus we neglected the subleading helicity components, which are suppressed by
powers of mW/Z/mX . Furthermore, we find fqq ≈ 65.5% at 8 TeV LHC, while it drops to
fqq ≈ 45.0% at 13 TeV LHC. We show the scaling behaviour of A in figure 8.
From figure 8, we can directly read off the expected cos(4Ψ) amplitude for our 8 TeV
and 13 TeV signal sample. Using ymin → 0 and ∆ηJJ, max →∞ the predicted amplitudes at
parton level match with A ≈ 0.014 at 8 TeV and A ≈ 0.0077 at 13 TeV very well our Monte
Carlo simulation. Including cuts we expect A ≈ 0.045 and A ≈ 0.034 for ATLAS and CMS
at 8 TeV, respectively, and A ≈ 0.021 for CMS at 13 TeV. For CMS the expected amplitude
is slightly larger than that seen in figure 7, which can be explained by the approximation
of eq. (3.3) used to relate cos θq with ymin.
4 Angular observables in semi-leptonic final states
We now turn to the semi-leptonic analyses, X → ``qq and X → `νqq, which provide impor-
tant cross-channels for a future discovery of a diboson resonance. To reiterate, the relative
rates of the 4q, ``qq, and `νqq final states will disentangle the intermediate W+W−, W±Z,
and ZZ nature of the resonance, which is very difficult to do using only the 4q analysis.
Moreover, the semileptonic channels enjoy cleaner reconstruction of angular observables,
larger signal efficiencies, and better control of systematic uncertainties, counterbalanced
by lower overall statistical power. The importance of the semileptonic channel, especially
– 19 –
JHEP09(2016)036
compared to the fully leptonic channel, was emphasized, for example, in refs. [126, 127].
In particular, the angular observables cos θp1 and cos θp3 , which were previously combined
into cos θq because we could not trace a given parent from one event to the next, are now
assigned as cos θq and cos θl. In addition, for the `νqq analysis, the cos θl distribution is
asymmetric because the charge of the lepton distinguishes leptons from the anti-lepton,
in constrast to the 4q case. We begin again by summarizing the semi-leptonic analyses
by ATLAS and CMS [11, 13, 14, 17, 19, 20] and then present the corresponding angular
distributions.
4.1 ATLAS and CMS semi-leptonic analyses at 8 TeV and 13 TeV
``qq Final State by ATLAS at 8 TeV. In the ``qq ATLAS analysis at 8 TeV, events
are required to have exactly two muons of opposite charge or two electrons, where muons
must have pT > 25 GeV and |η| < 2.4 and electrons must have pT > 25 GeV and |η| < 2.47,
excluding 1.37 < |η| < 1.52. In addition, all leptons must pass a track isolation (calorimeter
isolation) requirement (see ref. [13] for details). The lepton pair must have 66 GeV< m`` <
116 GeV and p``T > 400 GeV.
Jets are clustered using the C/A algorithm with R = 1.2 and need to have pT >
100 GeV and |η| < 1.2. One jet needs to survive the grooming procedure with ymin = 0.2025
and fulfill pT > 400 GeV and 70 GeV< m <110 GeV.
``qq Final State by CMS at 8 TeV. In the CMS 8 TeV ``qq analysis, electrons with
pT > 40 GeV and |η| < 2.5, excluding 1.44 < |η| < 1.56, muons with pT > 20 GeV and
|η| < 2.1 are selected, and all leptons must be isolated from other tracks as well as in the
calorimeter. Two same flavor, opposite charge, leptons are required, and for dimuon events,
the leading muon must have pT > 40 GeV. The lepton pair must have 70 GeV < m`` <
110 GeV.
Jets are reconstructed with the C/A algorithm using R = 0.8 and must have pT >
30 GeV and |η| < 2.4. They are pruned with zmin = 0.1 and are categorized by purity
according the N -subjettiness variable τ21, analogous to the CMS 4q search. The pruned
jet mass must lie within 65 GeV < mJ < 110 GeV. Both the leptonic and hadronic vector
boson candidates must have pVT > 80 GeV and satisfy mV V > 500 GeV. If there are multiple
hadronic V candidates, the hardest pT candidate in the higher purity category is used.
``qq Final State by ATLAS at 13 TeV. ATLAS uses the same kinematic acceptance
cuts on electrons and muons in the 13 TeV analysis as the 8 TeV analysis, and track isolation
requirements are imposed. Two muons of opposite charge or two electrons are required,
where the lepton pair must have 66 GeV < mµ+µ− < 116 GeV or 83 GeV< me+e− < 99 GeV,
respectively.
Jets are clustered using the anti-kT algorithm with R = 1.0 and are required to have
pT > 200 GeV and |η| < 2.0. The leading jet must satisfy the trimming procedure with
zmin = 0.05, and fulfill pJT > 0.4m``J and 68.2 GeV < mJ < 108.4 GeV. Additionally,
the jet needs to statisfy an upper bound on the D(β=1)2 energy correlator function. For
simplicity, we linearly interpolate the D2 cut between the two points quoted, D2 < 1.0 at
– 20 –
JHEP09(2016)036
pJT = 250 GeV and D2 < 1.8 at pJT = 1500 GeV. Finally, the dilepton system must have
p``T > 0.4m``J .
`νqq Final State by ATLAS at 8 TeV. In the 8 TeV ATLAS `νqq analsis, the lepton
kinematic criteria are the same as their 8 TeV ``qq search, and a similar isolation criteria
is used. Missing transverse energy /ET (MET) must exceed 30 GeV and is used to calculate
the corresponding neutrino four-momentum assuming no other source of MET and m2W =
(p` + pν)2:
pνz =1
2p`T
[(m2
W + 2~p `T · ~p ν
T )p `z ± E`
√(m2
W + 2~p `T · /~ET )2 − 4(p `
T )2 /E2T
]. (4.1)
In the case of two complex solutions for pνZ , the real part is used, otherwise the smaller
solution in absolute value is used. Events are required to have p`νT > 400 GeV.
Jets are clustered using the C/A algorithm with R = 1.2. One jet must survive
the grooming procedure with ymin = 0.2025 and fulfill pJT > 400 GeV, |η| < 2.0 and
65 GeV < mJ < 105 GeV, and the ∆φ between this jet and the MET vector must exceed
1. Events with at least one b-tagged jet are vetoed (see ref. [14] for details).
`νqq Final State by CMS at 8 TeV. At CMS, electrons with pT > 90 GeV and
|η| < 2.5, excluding 1.44 < |η| < 1.56, and muons with pT > 50 GeV and |η| < 2.1 are
selected. The same isolation criteria from the CMS ``qq search are applied. A single
muon or electron is required and MET must exceed 40 GeV or 80 GeV, respectively. The
corresponding neutrino four-momentum is reconstructed as in the ATLAS `νqq search, and
p`νT > 200 GeV is required.
Jets are reconstructed with the C/A algorithm using R = 0.8, pT > 30 and |η| < 2.4.
They are pruned with zmin = 0.1 and categorized by purity using τ21, as in the CMS 4q and
``qq searches. The pruned jet mass must again lie within 65 GeV < mJ < 110 GeV and have
pJT > 200 GeV, and if there are multiple hadronic V candidates, the hardest pT candidate
in the higher purity category is used. Furthermore, ∆RJ, (`ν) > π/2, ∆φJ, /ET > 2.0,
∆φJ, (`ν) > 2.0 and mJ`ν > 700 GeV are required. Events with one b-tagged jet are vetoed.
`νqq final state by ATLAS at 13 TeV. For the ATLAS 13 TeV `νqq search, leptons
are identified as in the ATLAS ``qq final state search at 8 TeV. Events must have one
lepton and /ET > 100 GeV, and the neutrino four-momentum is reconstructed as in the
8 TeV analysis.
Jets are clustered using the anti-kT algorithm with R = 1.0. The leading jet must
survive the trimming procedure with zmin = 0.05 and fulfill pT > 200 GeV, |η| < 2.0,
70.2 GeV < mJ < 106.4 GeV, and pJT > 0.4m`νJ . The same D(β=1)2 energy correlator cut
as the 13 TeV ``qq ATLAS search is imposed. Finally, events must have p`νT > 0.4m`νJ and
p`νT > 200 GeV, and events with b-tagged jets are vetoed.
`νqq final state by CMS at 13 TeV. Lastly, for the CMS `νqq search at 13 TeV, events
must have a single electron or muon, where electron candidates must have pT > 120 GeV
and |η| < 2.5, excluding 1.44 < |η| < 1.56, and muon candidates must have pT > 53 GeV
and |η| < 2.1. The same lepton isolation criteria as the CMS ``qq search are applied.
– 21 –
JHEP09(2016)036
Electron (muon) events must have at least 80 GeV (40 GeV) of MET. The neutrino four-
momentum is reconstructed as in the ATLAS `νqq final state search, and the lepton-
neutrino system must have p`νT > 200 GeV.
Jets are reconstructed with the anti-kT algorithm using R = 0.8, pT > 30 GeV and
|η| < 2.4. They are pruned with zmin = 0.1 and categorized by purity using the same
criteria as the 13 TeV CMS 4q search. To satisfy the boson tagging requirements, a pruned
jet J has to fulfill 65 GeV < mJ < 105 GeV and pJT > 200 GeV, and for events with
multiple hadronic boson candidates, the highest pT jet with the higher purity category
is used. Events must also pass ∆RJ, (`ν) > π/2, ∆φJ, /ET > 2.0, ∆φJ, (`ν) > 2.0, and
mJ`ν > 700 GeV cuts, and events with b-tagged jets are vetoed.
4.2 Angular observables in semi-leptonic final states and comparison with
fully hadronic final states
In figure 9, we show the normalized distributions for the cos θ∗, cos θq, cos θl, and Ψ angles
for the relevant ATLAS and CMS ``qq analyses. Note that we do not show the ``qq
background or the parton-level results in this plots. The ``qq final state mimics the 4q
final state, since the entire X → ``qq system is in principle reconstructible. Moreover, as
mentioned before, the cos θq distribution for the 4q final state splits into the new cos θqand cos θl angles, because the final state partons are distinguishable. On the other hand,
the ``qq final state pays an intrinsic penalty in statistical power, since the branching ratio
Br(W±Z → ``qq) / Br(W±Z → 4q) ≈ 0.094, for ` = e, µ, is only partially mitigated by
an improved semileptonic signal efficiency. Thus, the 4q and semileptonic channels play
important complementary roles both in the discovery of a new resonance but also give
significant cross-checks for spin discrimination.
From figure 9, we see that angular observables again provide important discrimination
power between spin-2 and the other spin hypotheses, while the main sensitivity to dis-
tinguish spin-0 from spin-1 resonances comes from the cos θ∗ angle. The sculpting effects
we identified earlier are still evident in cos θq as a result of the jet substructure cuts, but
on the other hand, most of the phase space is preserved for the cos θl distribution. Note
that there is no pT requirement on the individual subjets in contrast to the hard cut on
the lepton pT . This effectively flattens the cos θl shape for the spin-2 resonance compared
to cos θq, as events with large lepton pT imbalance near cos θl = ±1 tends to miss one of
the leptons.
One interesting feature is the sharp cliff in cos θ∗ for the ATLAS 13 TeV analysis, shown
in the top row, rightmost panel of figure 9. This is directly connected to the p``T > 0.4m``J
and pJT > 0.4m``J cuts, because from eq. (2.4), we see that the corresponding maximum
pseudorapidity gap between the vector boson candidates is ∆ηmax ∼ 2.1, which leads
to a maximum of | cos θ∗| = 0.6. We also note the ATLAS 8 TeV analysis has cliffs at
| cos(θ∗)| . 0.92 in the ATLAS 8 TeV analysis, driven by their milder cuts on p``T > 400 GeV
and pJT > 400 GeV.
In this regard, the most discrimination power between the various spin scenarios follows
from the CMS 8 TeV analysis, where the spin-0 and spin-2 curves are readily distinguished
– 22 –
JHEP09(2016)036
Figure 9. Normalized differential distributions for cos θ∗ (top row), cos θq (second row), cos θl(third row), and Ψ (bottom row) angles in the semi-leptonic final state ``qq, after imposing the
ATLAS 8 TeV (left column), CMS 8 TeV (middle), and ATLAS 13 TeV (right) analysis cuts.
– 23 –
JHEP09(2016)036
Figure 10. Normalized differential distributions for cos θ∗ (top row), cos θq (middle row), and
cos θl (bottom row), for the semi-leptonic final state `νqq, after imposing the ATLAS 8 TeV (first
column), CMS 8 TeV (second column), ATLAS 13 TeV (third column), and CMS 13 TeV (last
column) analysis cuts. We omit the Ψ angle as it does not have any significant discrimination
power.
from the spin-1 shapes. In contrast, the ATLAS 13 TeV analysis molds the cos θ∗ distribu-
tion to eliminate any possibility of distinguishing these different spins.
In figure 10, we show the normalized distributions for cos θ∗, cos θq, and cos θl for the
ATLAS and CMS 8 TeV and 13 TeV analyses. We remark that Ψ has no discriminating
power between the signal hypotheses, so we omit it from the figure. The cos θq distributions
are similar to those from before, while the cos θl shows a novel asymmetry.
The asymmetries in the cos θl distributions are the result of contamination by leptonic
τ decays. In particular, the extra neutrinos from the τ → eνν and τ → µνν decays skew
the reconstruction of the leptonic decay of the W±, where the additional neutrinos result in
a false reconstruction of the rest frame of the W±. This incorrect rest frame preferentially
groups the charged lepton used for the cos(θl) calculation closer to the boost vector needed
to move to the W± rest frame, skewing the cos θl distribution toward the +1 edge.
We also note, analogous to the ``qq final state, the clear cliffs in the cos θ∗ distribution
evident in the ATLAS 13 TeV analysis. These cliffs again arise from the p`νT > 0.4m`νJ and
pJT > 0.4m`νJ cuts, which effectively enforce a | cos θ∗| = 0.6 maximum, as discussed before.
– 24 –
JHEP09(2016)036
5 Projections for model discrimination from 4q final state
We now quantify the discrimination power between the different spin scenarios using the
CLs method [128] to test one signal against another in the 4q final state. We define one
signal resonance plus dijet background as a signal hypothesis, whereas the test hypothesis
is a different spin resonance plus the same dijet background. We use the differential shapes
| cos θ∗|, | cos θq|, and |Ψ| as individual discriminators as well as a likelihood combination
using all three observables.
We perform the pairwise signal hypothesis tests first using shape information alone and
second using both shape and rate information. The normalized differential distributions
serve as a first test for signal comparisons, because, by construction, different models for a
newly discovered resonance will have the same fiducial signal cross section in order to match
the observed excess. Hence, even if the 2 TeV excess seen by ATLAS with 8 TeV data is
not confirmed by the 13 TeV dataset, our shape-only spin comparisons are indicative of the
expected performance of different observables at the initial discovery stage. On the other
hand, if data from two different√s working points is available, then the expected scaling
from changes in parton distribution functions (PDFs) on various signal rates would be an
additional handle to discriminate between models.
Since we adopt the ATLAS 2 TeV diboson excess as our case study, we first normal-
ize the respective differential shapes to this excess. In a 300 GeV window centered at
mJJ = 2 TeV, the ATLAS collaboration observed an excess of 8 events over an expected
background of 8.94 events [8], where we quote the inclusive diboson tagging requirements.
We use this normalization factor, our simulated signal efficiencies, and our simulated PDF
rescaling factors to determine the expected number of signal events for each of the other
experimental analyses. In the shape only comparisons, the test hypothesis is always nor-
malized to the null hypothesis. The corresponding background expectations, again for
inclusive diboson selection cuts, are gleaned from each ATLAS and CMS analysis, albeit
with slightly shifted mass windows around the X mass.3 Since the current ATLAS 13 TeV
analysis does not show event counts for an inclusive diboson selection, we estimate the
inclusive background expectation from their available data, which we detail in appendix A.
Not surprisingly, the current discrimination power between different resonance spins
is low given the small signal statistics of the 8 TeV and 13 TeV analyses. This situation
is expected to dramatically improve, however, with 30 fb−1 luminosity of 13 TeV data. In
figure 11, we show the CLs values for a given null hypothesis and various test hypotheses
using the current ATLAS 13 TeV and CMS 13 TeV analyses [10, 11] rescaled for 30 fb−1 of
luminosity. We assume a 25% systematic uncertainty on the signal, and 30% on the dijet
background. In each row of each figure, the central exclusion limit using only differential
distributions is shown as a solid black line, and the corresponding 68% and 95% expected
C.L. exclusion limits are shown as the yellow and green bands. The dotted line in each
row shows the shift in the central expected exclusion limit if rate information is also added
in the signal hypothesis test. These C.L. results are not symmetric under interchange of
3We use the following invariant mass bins: [1850, 2150] GeV for ATLAS at 8 TeV, [1800, 2200] GeV for
ATLAS at 13 TeV, and [1852.3, 2136.4] GeV for CMS at 13 TeV.
– 25 –
JHEP09(2016)036
null hypothesis and test hypotheses, because in the shapes-only CLs analysis, the test
hypothesis is always scaled to the null hypothesis, and thus the S/B measure is not equal
under the interchange. When rates are included, the Poisson errors are not equal under
interchange, and so the resulting C.L. expectations are again not equal.
We see that the most discrimination power comes between the spin-0 and spin-1 cases
vs. the spin-2 case, which is expected from the clear distinctions in angular correlations
from figure 2 for cos θ∗, figure 4 for cos θq, as well as figure 7 for Ψ. In particular, the cos θqobservable provides significant discrimination, as the spin-2 concavity in the reconstructed
differential distribution is opposite that of the spin-0 and spin-1 resonances. We also
remark that the cos θq observable has twice the statistical power of the other cos θ∗ and
Ψ distributions because each event gives two reconstructed vector boson candidates, and
each vector boson candidate contributes one entry to the cos θq distribution.
We also see that CMS generally has stronger projected sensitivity than ATLAS, which
is a direct result of the different substructure analyses employed by each experiment. In
particular, the ATLAS 13 TeV analysis clusters large radius anti-kT jets with R = 1.0 and
trims these jets using a kT algorithm with R = 0.2 and hardness measure zmin = 0.05.
We have seen from figure 3 that the bulk of the quark pairs from X → V V → 4q decays
lie within ∆R = 0.2, which causes many of the nominal subjets to be merged at the
trimming stage.
As a result, the efficiency for the ATLAS 13 TeV analysis to identify two distinct subjets
is significantly lower than the corresponding CMS 13 TeV analysis, causing the overall
sensitivity to distinguishing spin hypotheses to suffer. The inclusion of rate information
shows strong discrimination between the spin-0 null hypothesis compared to the spin-
1 hypotheses. This simply follows from the fact that our ad-hoc, gluon-fusion induced,
spin-0 diboson resonance enjoys a significant PDF rescaling factor when going from 8 TeV
to 13 TeV. In contrast, the qq′-initiated Z ′, W ′, and WR spin-1 signals are all largely
indistinguishable when only considering the 4q final state. All of these spin-1 bosons
couple to the SM electroweak bosons using the same tree-level Lagrangian structure, which
makes it very difficult to disentangle by only considering the 4q excess. The small sensitivity
afforded by shape and rate information in distinguishing a Z ′ from a W ′ or WR explanation
comes from the different PDF scaling from 8 TeV to 13 TeV between qq′ vs. qq initial states.
We also note that our signal and background events use inclusive WW , WZ, and ZZ
hadronic diboson tags, and thus additional sensitivity to W ′ or WR discrimination from a
Z ′ signal would come from separating these diboson tagging categories.
In some cases, however, the inclusion of rate information decreases the overall discrimi-
nation power between signal hypotheses. This is because the shapes-only test magnifies the
importance of low event count bins where the signal to background ratio is high, whereas
the shapes and rates test loses discrimination power by having an overall lower significance
for the given signals. In particular, the linear rescaling we use for matching the signal rates
in the rates-only tests overcomes the Poisson statistics governing the low-count bins that
is otherwise dominant in the rates and shapes test.
Overall, we see that the spin-2 signal hypothesis will be tested at 95% C.L. using CMS
13 TeV cuts with 30 fb−1 luminosity. We also project 95% C.L. sensitivity between spin-0
– 26 –
JHEP09(2016)036
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(R
spin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 Z'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(+spin-0spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 Z'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(+spin-0
Rspin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(R
spin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 Z'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(+spin-0spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(R
spin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(+spin-0spin-1 Z'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(R
spin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 Z'+
spin-0
Null hyp. Test hyp. Discriminator C.L.10.10.010.001
-1ATLAS 13 TeV, 30 fb
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(R
spin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 Z'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(+spin-0spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 Z'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(+spin-0
Rspin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(R
spin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 Z'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(+spin-0spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(R
spin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(+spin-0spin-1 Z'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-2 y
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(R
spin-1 W
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 W'
combined
|Ψ|
)|qθ|cos(
*)|θ|cos(spin-1 Z'+
spin-0
Null hyp. Test hyp. Discriminator C.L.10.10.010.001
-1CMS 13 TeV, 30 fb
Figure 11. Projected spin sensitivity for the 13 TeV ATLAS (left) and CMS (right) analyses
with 30 fb−1 integrated luminosity. The long vertical dashed line indicates the 95% exclusion C.L.
Within each row, the solid black line and the green and yellow shaded areas denote the central
expected exclusion and the 68% and 95% likelihood expected exclusion intervals, using only shape
information. The dotted black line in each row shows the central expected exclusion limit including
rate information, using the 2 TeV excess as the normalization of the respective signal hypotheses.
– 27 –
JHEP09(2016)036
and other spin scenarios by combining rate information with the differential distributions.
If a new diboson resonance appears, however, the shape information alone from the current
13 TeV analyses would be insufficient to distinguish spin-0 from spin-1 possibilities.
We conclude this section by discussing the possible improvements to jet substruc-
ture analyses that could significantly help the prospects of signal discrimination in a fully
hadronic diboson final state. We have seen how the maximum ∆ηJJ cut introduces cliffs
in cos θ∗ that significantly cut away parts of phase space that would tell a spin-1 signal
from other possibilities. Allowing a looser ∆ηJJ cut, up to ∆ηJJ ≤ 2.2, for example, would
ensure that the extra sinuisoidal oscillation in the spin-2 hypothesis would be more eas-
ily distinguished compared to the spin-0 hypothesis and the dijet background, as seen in
figure 2. Although such a loose cut would lead to an immense increase in multijet back-
ground, even intermediate values of ∆ηJJ > 1.3 would already aid discrimination power
between the different spin hypotheses. We have also seen that the minimum subjet pTbalance requirement removes events above | cos θq| ≈ 0.66–0.90, depending on the ymin cut.
These events would have the best discrimination power between spin-2 signals and other
possibilities.
The most pernicious effect, however, comes from using a hard angular scale, such as the
kT reclustering with R = 0.2 inherent in the trimming procedure used by ATLAS 13 TeV
analysis. This hard angular scale not only causes distinct parton-level decays to merge into
single subjets, it also quashes the viability of a post-discovery analysis that builds angular
correlations from multiple subjets and introduces significant sculpting effects in cos θ∗ and
cos θq distributions. For our 2 TeV case study, the efficiency to find four distinct subjets
would increase significantly if a smaller reclustering radius of R = 0.15 were used, as seen
in figure 3, but the minimum radius for a given resonance mass hypothesis with mass mX
can be estimated from Rmin . 2mW/Z/pT,X ∼ mW/Z/mX .
A jet substructure method optimized for both signal discovery and post-discovery sig-
nal discrimination would ameliorate these negative effects. The subjet pT balance require-
ment and alternate reclustering methods that do not introduce a hard angular scale are
thus the most motivated details to modify for a spin-sensitive jet substructure optimization.
We reserve a study to address these questions for future work.
6 Conclusion
We have performed a comprehensive study of how angular correlations in resonance decays
to four quarks can be preserved, albeit distorted, after effects from hadronization and
showering, detector resolution, jet clustering, and W and Z tagging via currently employed
jet substructure techniques. We have connected the observed cliffs in cos θ∗ to cuts on the
maximum pseudorapidity difference between the parent fat jets, the deficit of events around
cos θ∗, cos θq ≈ 0 to the hard angular scale used in the reclustering of subjets, and the
removal of events above cos θq ≈ 0.66–0.90 to the subjet pT balance requirement employed
by the various analyses. We have also emphasized the importance of small angular scales for
jet substructure reclustering, having seen how large reclustering radii merge distinct decay
– 28 –
JHEP09(2016)036
products of highly boosted vector parents and resulting sensitivity to spin discrimination
is greatly reduced.
We recognize that spin discrimination of a new resonance in diboson decays is one
facet of a possible post-discovery signal characterization effort. In particular, some of
the degeneracies among the various spin-1 signal hypotheses can only be distinguished by
observing semi-leptonic diboson decays as well as additional direct decays to fermions. The
rates for the latter decays are model dependent features of each given signal hypothesis. In
the special case of the 2 TeV excess seen by ATLAS in 8 TeV data, additional discrimination
power between possible new physics resonances is afforded by the simple fact that the LHC
is now operating at 13 TeV. The different production modes for spin-0, spin-1 neutral,
spin-1 charged, and spin-2 resonances obviously scale differently going from√s = 8 TeV to√
s = 13 TeV, which establishes benchmark expected significances for the different signals
as a function of luminosity.
Our work, however, addresses the more general question about the feasibility of using
an analysis targetting a resonance in a fully hadronic diboson decay for spin and parity
discrimination. It also provides a method for distinguishing longitudinal versus transverse
polarizations of electroweak gauge bosons, which is an intrinsic element of analyses aimed
at probing unitarity of electroweak boson scattering. A future work will tackle the question
of an optimized jet substructure analysis that avoids introducing significant distortions in
angular observables and hence enhances the possible spin sensitivity beyond the projections
shown in figure 11. We also plan to investigate angular correlations in fully hadronic
final states with intermediate new physics resonances, as well as the viability of angular
observables using Higgs and top substructure methods. Even without any improvement,
a spin-2 explanation for the 2 TeV excess will be tested at the 95% C.L. from other spin
hypotheses with 30 fb−1 of 13 TeV luminosity using only shape information, while spin-0
vs. spin-1 discrimination would come from the combination of rate and shape information.
Acknowledgments
We would like to thank Michael Baker, Ian Lewis, Adam Martin, Jesse Thaler, Andrea
Thamm, Nhan Tran, and Yuhsin Tsai, for useful discussions, and Riccardo Torre, Andrea
Thamm for use of the Heavy Vector Triplets FeynRules model and Bogdan Dobrescu and
Patrick Fox for use of the right-handed WR model. This research is supported by the
Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter
(PRISMA-EXC 1098). The work of MB is moreover supported by the German Research
Foundation (DFG) in the framework of the Research Unit New Physics at the Large Hadron
Collider” (FOR 2239).
A ATLAS 13 TeV background extraction, inclusive diboson selection
For our projections on spin sensitivity at 13 TeV LHC, we require the background estimate
for inclusive diboson selection cuts. As the current ATLAS 13 TeV analysis [10] only
– 29 –
JHEP09(2016)036
provides WW , WZ, and ZZ event counts, which are not exclusive selection bins because
of overlapping W and Z mass windows, we extract the inclusive number of events as follows.
For the mass range 1.0 TeV < mJJ < 2.5 TeV, the ATLAS analysis specifies that
38 events lie in the overlap region and contribute to all three channels. We thus assign
p ≈√
38/N as a flat probability for an event with a W -tag to also be a Z-tagged event and
vice versa, where N is the number of events passing inclusive diboson tagging requirements.
We can write N = NW 0Z0 + NW 0W 0 + NZ0Z0 , where each category is defined exclusively
and without overlap. Then,
N = NWZ +NWW +NZZ
−NW 0Z0 ·[P(Z in overlap region) + P(W in overlap region)
+ 2P(W and Z in overlap region)]
−NW 0W 0 · [P(one W in overlap region) + 2P(both W in overlap region)]
−NZ0Z0 · [P(one Z in overlap region) + 2P(both Z in overlap region)] , (A.1)
where factors of 2 in eq. (A.1) reflect the fact that this particular event contributes to all
three categories and therefore two events need to be subtracted from the total sum. From
the ATLAS analysis [10], we have NWZ +NWW +NZZ = 300, thus
N = 300−NW 0Z0
[p(1− p) + p(1− p) + 2p2
]−NW 0W 0
[2p(1− p) + 2p2
]−NZ0Z0
[2p(1− p) + 2p2
]= 300− 2Np . (A.2)
Using p ≈√
38/N , and solving for N , we obtain N ≈ 149, and thus 75 events fall into
two diboson categories and 38 events are triply counted, which is very similar to the
breakdown of double and triple counted events in the ATLAS 8 TeV analysis [8]. We use
this fraction to estimate the expected number of background events passing the inclusive
diboson tagging requirements.
Open Access. This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
References
[1] J.M. Butterworth, A.R. Davison, M. Rubin and G.P. Salam, Jet substructure as a new
Higgs search channel at the LHC, Phys. Rev. Lett. 100 (2008) 242001 [arXiv:0802.2470]
[INSPIRE].
[2] A. Abdesselam et al., Boosted objects: a probe of beyond the standard model physics, Eur.
Phys. J. C 71 (2011) 1661 [arXiv:1012.5412] [INSPIRE].
[3] A. Altheimer et al., Jet substructure at the Tevatron and LHC: new results, new tools, new
benchmarks, J. Phys. G 39 (2012) 063001 [arXiv:1201.0008] [INSPIRE].
– 30 –
JHEP09(2016)036
[4] A. Altheimer et al., Boosted objects and jet substructure at the LHC. Report of
BOOST2012, held at IFIC Valencia, 23rd-27th of July 2012, Eur. Phys. J. C 74 (2014)
2792 [arXiv:1311.2708] [INSPIRE].
[5] D. Adams et al., Towards an understanding of the correlations in jet substructure, Eur.
Phys. J. C 75 (2015) 409 [arXiv:1504.00679] [INSPIRE].
[6] ATLAS collaboration, Jet mass and substructure of inclusive jets in√s = 7 TeV pp
collisions with the ATLAS experiment, JHEP 05 (2012) 128 [arXiv:1203.4606] [INSPIRE].
[7] ATLAS collaboration, Performance of jet substructure techniques for large-R jets in
proton-proton collisions at√s = 7 TeV using the ATLAS detector, JHEP 09 (2013) 076
[arXiv:1306.4945] [INSPIRE].
[8] ATLAS collaboration, Search for high-mass diboson resonances with boson-tagged jets in
proton-proton collisions at√s = 8 TeV with the ATLAS detector, JHEP 12 (2015) 055
[arXiv:1506.00962] [INSPIRE].
[9] CMS collaboration, Search for massive resonances in dijet systems containing jets tagged
as W or Z boson decays in pp collisions at√s = 8 TeV, JHEP 08 (2014) 173
[arXiv:1405.1994] [INSPIRE].
[10] ATLAS collaboration, Search for resonances with boson-tagged jets in 3.2 fb−1 of pp
collisions at√s = 13 TeV collected with the ATLAS detector, ATLAS-CONF-2015-073
(2015).
[11] CMS Collaboration, Search for massive resonances decaying into pairs of boosted W and Z
bosons at√s = 13 TeV, CMS-PAS-EXO-15-002 (2015).
[12] ATLAS collaboration, Search for WZ resonances in the fully leptonic channel using pp
collisions at√s = 8 TeV with the ATLAS detector, Phys. Lett. B 737 (2014) 223
[arXiv:1406.4456] [INSPIRE].
[13] ATLAS collaboration, Search for resonant diboson production in the ``qq final state in pp
collisions at√s = 8 TeV with the ATLAS detector, Eur. Phys. J. C 75 (2015) 69
[arXiv:1409.6190] [INSPIRE].
[14] ATLAS collaboration, Search for production of WW/WZ resonances decaying to a lepton,
neutrino and jets in pp collisions at√s = 8 TeV with the ATLAS detector, Eur. Phys. J. C
75 (2015) 209 [Erratum ibid. C 75 (2015) 370] [arXiv:1503.04677] [INSPIRE].
[15] ATLAS collaboration, Combination of searches for WW , WZ and ZZ resonances in pp
collisions at√s = 8 TeV with the ATLAS detector, Phys. Lett. B 755 (2016) 285
[arXiv:1512.05099] [INSPIRE].
[16] CMS collaboration, Search for new resonances decaying via WZ to leptons in proton-proton
collisions at√s = 8 TeV, Phys. Lett. B 740 (2015) 83 [arXiv:1407.3476] [INSPIRE].
[17] CMS collaboration, Search for massive resonances decaying into pairs of boosted bosons in
semi-leptonic final states at√s = 8 TeV, JHEP 08 (2014) 174 [arXiv:1405.3447]
[INSPIRE].
[18] J. Brehmer et al., The diboson excess: experimental situation and classification of
explanations; a Les Houches pre-proceeding, arXiv:1512.04357 [INSPIRE].
[19] ATLAS collaboration, Search for WW/WZ resonance production in the `νqq final state at√s = 13 TeV with the ATLAS detector at the LHC, ATLAS-CONF-2015-075 (2015).
– 31 –
JHEP09(2016)036
[20] ATLAS collaboration, Search for diboson resonances in the llqq final state in pp collisions
at√s = 13 TeV with the ATLAS detector, ATLAS-CONF-2015-071 (2015).
[21] ATLAS collaboration, Search for diboson resonances in the ννqq final state in pp collisions
at√s = 13 TeV with the ATLAS detector, ATLAS-CONF-2015-068 (2015).
[22] B.A. Dobrescu and Z. Liu, W ′ boson near 2 TeV: predictions for Run 2 of the LHC, Phys.
Rev. Lett. 115 (2015) 211802 [arXiv:1506.06736] [INSPIRE].
[23] B.A. Dobrescu and Z. Liu, Heavy Higgs bosons and the 2 TeV W ′ boson, JHEP 10 (2015)
118 [arXiv:1507.01923] [INSPIRE].
[24] J. Brehmer, J. Hewett, J. Kopp, T. Rizzo and J. Tattersall, Symmetry restored in dibosons
at the LHC?, JHEP 10 (2015) 182 [arXiv:1507.00013] [INSPIRE].
[25] B.A. Dobrescu and P.J. Fox, Signals of a 2 TeV W ′ boson and a heavier Z ′ boson, JHEP
05 (2016) 047 [arXiv:1511.02148] [INSPIRE].
[26] L.A. Anchordoqui et al., Stringy origin of diboson and dijet excesses at the LHC, Phys.
Lett. B 749 (2015) 484 [arXiv:1507.05299] [INSPIRE].
[27] ATLAS collaboration, Search for new phenomena in the dijet mass distribution using pp
collision data at√s = 8 TeV with the ATLAS detector, Phys. Rev. D 91 (2015) 052007
[arXiv:1407.1376] [INSPIRE].
[28] CMS collaboration, Search for resonances and quantum black holes using dijet mass spectra
in proton-proton collisions at√s = 8 TeV, Phys. Rev. D 91 (2015) 052009
[arXiv:1501.04198] [INSPIRE].
[29] ATLAS collaboration, Search for new phenomena in dijet mass and angular distributions
from pp collisions at√s = 13 TeV with the ATLAS detector, Phys. Lett. B 754 (2016) 302
[arXiv:1512.01530] [INSPIRE].
[30] CMS collaboration, Search for narrow resonances decaying to dijets in proton-proton
collisions at√s = 13 TeV, Phys. Rev. Lett. 116 (2016) 071801 [arXiv:1512.01224]
[INSPIRE].
[31] ATLAS collaboration, Search for a new resonance decaying to a W or Z boson and a Higgs
boson in the ``/`ν/νν + bb final states with the ATLAS detector, Eur. Phys. J. C 75 (2015)
263 [arXiv:1503.08089] [INSPIRE].
[32] CMS collaboration, Search for narrow high-mass resonances in proton-proton collisions at√s = 8 TeV decaying to a Z and a Higgs boson, Phys. Lett. B 748 (2015) 255
[arXiv:1502.04994] [INSPIRE].
[33] CMS collaboration, Search for a massive resonance decaying into a Higgs boson and a W
or Z boson in hadronic final states in proton-proton collisions at√s = 8 TeV, JHEP 02
(2016) 145 [arXiv:1506.01443] [INSPIRE].
[34] CMS collaboration, Search for massive WH resonances decaying into the `νbb final state at√s = 8 TeV, Eur. Phys. J. C 76 (2016) 237 [arXiv:1601.06431] [INSPIRE].
[35] ATLAS collaboration, Search for new resonances decaying to a W or Z boson and a Higgs
boson in the ``bb, `νbb and ννbb channels in pp collisions at√s = 13 TeV with the ATLAS
detector, ATLAS-CONF-2015-074 (2015).
[36] C.-H. Chen and T. Nomura, Diboson excess in the Higgs singlet and vectorlike quark
models, Phys. Rev. D 92 (2015) 115021 [arXiv:1509.02039] [INSPIRE].
– 32 –
JHEP09(2016)036
[37] C.-H. Chen and T. Nomura, 2 TeV Higgs boson and diboson excess at the LHC, Phys. Lett.
B 749 (2015) 464 [arXiv:1507.04431] [INSPIRE].
[38] Y. Omura, K. Tobe and K. Tsumura, Survey of Higgs interpretations of the diboson
excesses, Phys. Rev. D 92 (2015) 055015 [arXiv:1507.05028] [INSPIRE].
[39] W. Chao, ATLAS diboson excesses from the stealth doublet model, Phys. Lett. B 753 (2016)
117 [arXiv:1507.05310] [INSPIRE].
[40] D. Aristizabal Sierra, J. Herrero-Garcia, D. Restrepo and A. Vicente, Diboson anomaly:
heavy Higgs resonance and QCD vectorlike exotics, Phys. Rev. D 93 (2016) 015012
[arXiv:1510.03437] [INSPIRE].
[41] C. Petersson and R. Torre, ATLAS diboson excess from low scale supersymmetry breaking,
JHEP 01 (2016) 099 [arXiv:1508.05632] [INSPIRE].
[42] B.C. Allanach, P.S.B. Dev and K. Sakurai, ATLAS diboson excess could be an R-parity
violating dismuon excess, Phys. Rev. D 93 (2016) 035010 [arXiv:1511.01483] [INSPIRE].
[43] C.-W. Chiang, H. Fukuda, K. Harigaya, M. Ibe and T.T. Yanagida, Diboson resonance as a
portal to hidden strong dynamics, JHEP 11 (2015) 015 [arXiv:1507.02483] [INSPIRE].
[44] G. Cacciapaglia, A. Deandrea and M. Hashimoto, Scalar hint from the diboson excess?,
Phys. Rev. Lett. 115 (2015) 171802 [arXiv:1507.03098] [INSPIRE].
[45] H.S. Fukano, M. Kurachi, S. Matsuzaki, K. Terashi and K. Yamawaki, 2 TeV walking
Technirho at LHC?, Phys. Lett. B 750 (2015) 259 [arXiv:1506.03751] [INSPIRE].
[46] D. Buarque Franzosi, M.T. Frandsen and F. Sannino, Diboson signals via Fermi scale
spin-one states, Phys. Rev. D 92 (2015) 115005 [arXiv:1506.04392] [INSPIRE].
[47] A. Thamm, R. Torre and A. Wulzer, Composite heavy vector triplet in the ATLAS diboson
excess, Phys. Rev. Lett. 115 (2015) 221802 [arXiv:1506.08688] [INSPIRE].
[48] L. Bian, D. Liu and J. Shu, Low scale composite Higgs model and 1.8 ∼ 2 TeV diboson
excess, arXiv:1507.06018 [INSPIRE].
[49] H. Fritzsch, Composite weak bosons at the LHC, arXiv:1507.06499 [INSPIRE].
[50] K. Lane and L. Pritchett, Heavy vector partners of the light composite Higgs, Phys. Lett. B
753 (2016) 211 [arXiv:1507.07102] [INSPIRE].
[51] M. Low, A. Tesi and L.-T. Wang, Composite spin-1 resonances at the LHC, Phys. Rev. D
92 (2015) 085019 [arXiv:1507.07557] [INSPIRE].
[52] H.S. Fukano, S. Matsuzaki, K. Terashi and K. Yamawaki, Conformal barrier and hidden
local symmetry constraints: walking technirhos in LHC diboson channels, Nucl. Phys. B
904 (2016) 400 [arXiv:1510.08184] [INSPIRE].
[53] G. Cacciapaglia and M.T. Frandsen, Unitarity implications of a diboson resonance in the
TeV region for Higgs physics, Phys. Rev. D 92 (2015) 055035 [arXiv:1507.00900]
[INSPIRE].
[54] B.C. Allanach, B. Gripaios and D. Sutherland, Anatomy of the ATLAS diboson anomaly,
Phys. Rev. D 92 (2015) 055003 [arXiv:1507.01638] [INSPIRE].
[55] L. Bian, D. Liu, J. Shu and Y. Zhang, Interference effect on resonance studies in searches
of heavy particles, Int. J. Mod. Phys. 31 (2016) 1650083 [arXiv:1509.02787] [INSPIRE].
– 33 –
JHEP09(2016)036
[56] B. Bhattacherjee, P. Byakti, C.K. Khosa, J. Lahiri and G. Mendiratta, Alternative search
strategies for a BSM resonance fitting the ATLAS diboson excess, Phys. Rev. D 93 (2016)
075015 [arXiv:1511.02797] [INSPIRE].
[57] S.-S. Xue, Vectorlike W±-boson coupling at TeV and third family fermion masses, Phys.
Rev. D 93 (2016) 073001 [arXiv:1506.05994] [INSPIRE].
[58] Y. Gao, T. Ghosh, K. Sinha and J.-H. Yu, SU(2) × SU(2)×U(1) interpretations of the
diboson and Wh excesses, Phys. Rev. D 92 (2015) 055030 [arXiv:1506.07511] [INSPIRE].
[59] J. Heeck and S. Patra, Minimal left-right symmetric dark matter, Phys. Rev. Lett. 115
(2015) 121804 [arXiv:1507.01584] [INSPIRE].
[60] P.S. Bhupal Dev and R.N. Mohapatra, Unified explanation of the eejj, diboson and dijet
resonances at the LHC, Phys. Rev. Lett. 115 (2015) 181803 [arXiv:1508.02277] [INSPIRE].
[61] F.F. Deppisch et al., Reconciling the 2 TeV excesses at the LHC in a linear seesaw left-right
model, Phys. Rev. D 93 (2016) 013011 [arXiv:1508.05940] [INSPIRE].
[62] U. Aydemir, D. Minic, C. Sun and T. Takeuchi, Pati-Salam unification from
noncommutative geometry and the TeV-scale WR boson, Int. J. Mod. Phys. A 31 (2016)
1550223 [arXiv:1509.01606] [INSPIRE].
[63] R.L. Awasthi, P.S.B. Dev and M. Mitra, Implications of the diboson excess for neutrinoless
double beta decay and lepton flavor violation in TeV scale left right symmetric model, Phys.
Rev. D 93 (2016) 011701 [arXiv:1509.05387] [INSPIRE].
[64] P. Ko and T. Nomura, SU(2)L × SU(2)R minimal dark matter with 2 TeV W ′, Phys. Lett.
B 753 (2016) 612 [arXiv:1510.07872] [INSPIRE].
[65] J.H. Collins and W.H. Ng, A 2 TeV WR, supersymmetry and the Higgs mass, JHEP 01
(2016) 159 [arXiv:1510.08083] [INSPIRE].
[66] J.A. Aguilar-Saavedra and F.R. Joaquim, Multiboson production in W ′ decays, JHEP 01
(2016) 183 [arXiv:1512.00396] [INSPIRE].
[67] U. Aydemir, SO(10) grand unification in light of recent LHC searches and colored scalars at
the TeV-scale, Int. J. Mod. Phys. A 31 (2016) 1650034 [arXiv:1512.00568] [INSPIRE].
[68] J.L. Evans, N. Nagata, K.A. Olive and J. Zheng, The ATLAS diboson resonance in
non-supersymmetric SO(10), JHEP 02 (2016) 120 [arXiv:1512.02184] [INSPIRE].
[69] A. Das, N. Nagata and N. Okada, Testing the 2 TeV resonance with trileptons, JHEP 03
(2016) 049 [arXiv:1601.05079] [INSPIRE].
[70] J. Hisano, N. Nagata and Y. Omura, Interpretations of the ATLAS diboson resonances,
Phys. Rev. D 92 (2015) 055001 [arXiv:1506.03931] [INSPIRE].
[71] A. Alves, A. Berlin, S. Profumo and F.S. Queiroz, Dirac-fermionic dark matter in U(1)Xmodels, JHEP 10 (2015) 076 [arXiv:1506.06767] [INSPIRE].
[72] A.E. Faraggi and M. Guzzi, Extra Z ′s and W ′s in heterotic-string derived models, Eur.
Phys. J. C 75 (2015) 537 [arXiv:1507.07406] [INSPIRE].
[73] T. Li, J.A. Maxin, V.E. Mayes and D.V. Nanopoulos, Diboson excesses in leptophobic
U(1)LP models from string theories, Phys. Rev. D 93 (2016) 045007 [arXiv:1509.06821]
[INSPIRE].
[74] Z.-W. Wang, F.S. Sage, T.G. Steele and R.B. Mann, Asymptotic safety in the conformal
hidden sector?, arXiv:1511.02531 [INSPIRE].
– 34 –
JHEP09(2016)036
[75] B. Allanach, F.S. Queiroz, A. Strumia and S. Sun, Z ′ models for the LHCb and g − 2 muon
anomalies, Phys. Rev. D 93 (2016) 055045 [arXiv:1511.07447] [INSPIRE].
[76] W.-Z. Feng, Z. Liu and P. Nath, ATLAS diboson excess from Stueckelberg mechanism,
JHEP 04 (2016) 090 [arXiv:1511.08921] [INSPIRE].
[77] K. Cheung, W.-Y. Keung, P.-Y. Tseng and T.-C. Yuan, Interpretations of the ATLAS
diboson anomaly, Phys. Lett. B 751 (2015) 188 [arXiv:1506.06064] [INSPIRE].
[78] Q.-H. Cao, B. Yan and D.-M. Zhang, Simple non-abelian extensions of the standard model
gauge group and the diboson excesses at the LHC, Phys. Rev. D 92 (2015) 095025
[arXiv:1507.00268] [INSPIRE].
[79] T. Abe, R. Nagai, S. Okawa and M. Tanabashi, Unitarity sum rules, three-site moose model
and the ATLAS 2 TeV diboson anomalies, Phys. Rev. D 92 (2015) 055016
[arXiv:1507.01185] [INSPIRE].
[80] T. Abe, T. Kitahara and M.M. Nojiri, Prospects for spin-1 resonance search at 13 TeV
LHC and the ATLAS diboson excess, JHEP 02 (2016) 084 [arXiv:1507.01681] [INSPIRE].
[81] H.S. Fukano, S. Matsuzaki and K. Yamawaki, Conformal barrier for new vector bosons
decay to the Higgs, Mod. Phys. Lett. A 31 (2016) 1630009 [arXiv:1507.03428] [INSPIRE].
[82] T. Appelquist, Y. Bai, J. Ingoldby and M. Piai, Spectrum-doubled heavy vector bosons at
the LHC, JHEP 01 (2016) 109 [arXiv:1511.05473] [INSPIRE].
[83] K. Das, T. Li, S. Nandi and S.K. Rai, Diboson excesses in an anomaly free leptophobic
left-right model, Phys. Rev. D 93 (2016) 016006 [arXiv:1512.00190] [INSPIRE].
[84] V. Sanz, On the compatibility of the diboson excess with a gg-initiated composite sector,
Adv. High Energy Phys. 2016 (2016) 3279568 [arXiv:1507.03553] [INSPIRE].
[85] H. Terazawa and M. Yasue, Excited gauge and Higgs bosons in the unified composite model,
Nonlin. Phenom. Complex Syst. 19 (2016) 1 [arXiv:1508.00172] [INSPIRE].
[86] J.A. Aguilar-Saavedra, Triboson interpretations of the ATLAS diboson excess, JHEP 10
(2015) 099 [arXiv:1506.06739] [INSPIRE].
[87] H.M. Lee, D. Kim, K. Kong and S.C. Park, Diboson excesses demystified in effective field
theory approach, JHEP 11 (2015) 150 [arXiv:1507.06312] [INSPIRE].
[88] S.P. Liew and S. Shirai, Testing ATLAS diboson excess with dark matter searches at LHC,
JHEP 11 (2015) 191 [arXiv:1507.08273] [INSPIRE].
[89] P. Arnan, D. Espriu and F. Mescia, Interpreting a 2 TeV resonance in WW scattering,
Phys. Rev. D 93 (2016) 015020 [arXiv:1508.00174] [INSPIRE].
[90] S. Fichet and G. von Gersdorff, Effective theory for neutral resonances and a statistical
dissection of the ATLAS diboson excess, JHEP 12 (2015) 089 [arXiv:1508.04814]
[INSPIRE].
[91] A. Sajjad, Understanding diboson anomalies, Phys. Rev. D 93 (2016) 055028
[arXiv:1511.02244] [INSPIRE].
[92] ATLAS collaboration, Study of the spin and parity of the Higgs boson in diboson decays
with the ATLAS detector, Eur. Phys. J. C 75 (2015) 476 [arXiv:1506.05669] [INSPIRE].
[93] ATLAS collaboration, Measurements of the Higgs boson production and decay rates and
coupling strengths using pp collision data at√s = 7 and 8 TeV in the ATLAS experiment,
Eur. Phys. J. C 76 (2016) 6 [arXiv:1507.04548] [INSPIRE].
– 35 –
JHEP09(2016)036
[94] CMS collaboration, Constraints on the spin-parity and anomalous HVV couplings of the
Higgs boson in proton collisions at 7 and 8 TeV, Phys. Rev. D 92 (2015) 012004
[arXiv:1411.3441] [INSPIRE].
[95] CMS collaboration, Precise determination of the mass of the Higgs boson and tests of
compatibility of its couplings with the standard model predictions using proton collisions at 7
and 8 TeV, Eur. Phys. J. C 75 (2015) 212 [arXiv:1412.8662] [INSPIRE].
[96] N. Cabibbo and A. Maksymowicz, Angular correlations in Ke4 decays and determination of
low-energy π-π phase shifts, Phys. Rev. B 438 (1965) 137 [Erratum ibid. 168 (1968) 1926].
[97] J.R. Dell’aquila and C.A. Nelson, P or CP determination by sequential decays: V1V2 modes
with decays into `−A`B and/or q−AqB , Phys. Rev. D 33 (1986) 80.
[98] J.R. Dell’aquila and C.A. Nelson, Distinguishing a spin-0 technipion and an elementary
Higgs boson: V1V2 modes with decays into `−A`B and/or q−AqB , Phys. Rev. D 33 (1986) 93.
[99] C.A. Nelson, Correlation between decay planes in Higgs-boson decays into a W pair (into a
Z pair), Phys. Rev. D 37 (1988) 1220.
[100] Y. Gao, A.V. Gritsan, Z. Guo, K. Melnikov, M. Schulze and N.V. Tran, Spin determination
of single-produced resonances at hadron colliders, Phys. Rev. D 81 (2010) 075022
[arXiv:1001.3396] [INSPIRE].
[101] S. Bolognesi et al., On the spin and parity of a single-produced resonance at the LHC, Phys.
Rev. D 86 (2012) 095031 [arXiv:1208.4018] [INSPIRE].
[102] Y. Chen, N. Tran and R. Vega-Morales, Scrutinizing the Higgs signal and background in the
2e2µ golden channel, JHEP 01 (2013) 182 [arXiv:1211.1959] [INSPIRE].
[103] Y. Chen et al., 8D likelihood effective Higgs couplings extraction framework in h→ 4`,
JHEP 01 (2015) 125 [arXiv:1401.2077] [INSPIRE].
[104] Y. Chen et al., Technical note for 8D likelihood effective Higgs couplings extraction
framework in the golden channel, arXiv:1410.4817 [INSPIRE].
[105] Y.L. Dokshitzer, G.D. Leder, S. Moretti and B.R. Webber, Better jet clustering algorithms,
JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].
[106] S.D. Ellis, C.K. Vermilion and J.R. Walsh, Techniques for improved heavy particle searches
with jet substructure, Phys. Rev. D 80 (2009) 051501 [arXiv:0903.5081] [INSPIRE].
[107] S.D. Ellis, C.K. Vermilion and J.R. Walsh, Recombination algorithms and jet substructure:
pruning as a tool for heavy particle searches, Phys. Rev. D 81 (2010) 094023
[arXiv:0912.0033] [INSPIRE].
[108] J. Thaler and K. Van Tilburg, Identifying boosted objects with N-subjettiness, JHEP 03
(2011) 015 [arXiv:1011.2268] [INSPIRE].
[109] J. Thaler and K. Van Tilburg, Maximizing boosted top identification by minimizing
N-subjettiness, JHEP 02 (2012) 093 [arXiv:1108.2701] [INSPIRE].
[110] D. Krohn, J. Thaler and L.-T. Wang, Jet trimming, JHEP 02 (2010) 084
[arXiv:0912.1342] [INSPIRE].
[111] S. Catani et al., Longitudinally-invariant k⊥-clustering algorithms for hadron-hadron
collisions, Nucl. Phys. B 406 (1993) 187.
[112] A.J. Larkoski, G.P. Salam and J. Thaler, Energy correlation functions for jet substructure,
JHEP 06 (2013) 108 [arXiv:1305.0007] [INSPIRE].
– 36 –
JHEP09(2016)036
[113] A.J. Larkoski, I. Moult and D. Neill, Power counting to better jet observables, JHEP 12
(2014) 009 [arXiv:1409.6298] [INSPIRE].
[114] A.J. Larkoski, I. Moult and D. Neill, Analytic boosted boson discrimination, JHEP 05
(2016) 117 [arXiv:1507.03018] [INSPIRE].
[115] A. Alloul, N.D. Christensen, C. Degrande, C. Duhr and B. Fuks, FeynRules 2.0 — A
complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250
[arXiv:1310.1921] [INSPIRE].
[116] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, MadGraph 5: going beyond,
JHEP 06 (2011) 128 [arXiv:1106.0522] [INSPIRE].
[117] D. Pappadopulo, A. Thamm, R. Torre and A. Wulzer, Heavy vector triplets: bridging theory
and data, JHEP 09 (2014) 060 [arXiv:1402.4431] [INSPIRE].
[118] L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys.
Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
[119] L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999)
4690 [hep-th/9906064] [INSPIRE].
[120] K. Hagiwara, J. Kanzaki, Q. Li and K. Mawatari, HELAS and MadGraph/MadEvent with
spin-2 particles, Eur. Phys. J. C 56 (2008) 435 [arXiv:0805.2554] [INSPIRE].
[121] T. Sjostrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015)
159 [arXiv:1410.3012] [INSPIRE].
[122] DELPHES 3 collaboration, J. de Favereau et al., DELPHES 3, a modular framework for
fast simulation of a generic collider experiment, JHEP 02 (2014) 057 [arXiv:1307.6346]
[INSPIRE].
[123] M. Cacciari, G.P. Salam and G. Soyez, FastJet user manual, Eur. Phys. J. C 72 (2012)
1896 [arXiv:1111.6097] [INSPIRE].
[124] M. Cacciari, G.P. Salam and G. Soyez, The anti-kt jet clustering algorithm, JHEP 04
(2008) 063 [arXiv:0802.1189] [INSPIRE].
[125] CMS collaboration, Identification techniques for highly boosted W bosons that decay into
hadrons, JHEP 12 (2014) 017 [arXiv:1410.4227] [INSPIRE].
[126] C. Hackstein and M. Spannowsky, Boosting Higgs discovery: the forgotten channel, Phys.
Rev. D 82 (2010) 113012 [arXiv:1008.2202] [INSPIRE].
[127] C. Englert, C. Hackstein and M. Spannowsky, Measuring spin and CP from semi-hadronic
ZZ decays using jet substructure, Phys. Rev. D 82 (2010) 114024 [arXiv:1010.0676]
[INSPIRE].
[128] A.L. Read, Advanced statistical techniques in particle physics. Proceedings, Conference,
Durham, U.K., March 18–22, 2002, J. Phys. G 28 (2002) 2693.
– 37 –